Generalized inverses of matrices over skew polynomial rings
| dc.contributor.author | Feng, Qiwei | |
| dc.contributor.examiningcommittee | Kucera, Tommy (Mathematics) Mandal, Saumen (Statistics) | en_US |
| dc.contributor.supervisor | Zhang, Yang (Mathematics) | en_US |
| dc.date.accessioned | 2017-03-30T14:34:52Z | |
| dc.date.available | 2017-03-30T14:34:52Z | |
| dc.date.issued | 2017 | |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Science (M.Sc.) | en_US |
| dc.description.abstract | The applications of generalized inverses of matrices appear in many fields like applied mathematics, statistics and engineering [2]. In this thesis, we discuss generalized inverses of matrices over Ore polynomial rings (also called Ore matrices). We first introduce some necessary and sufficient conditions for the existence of {1}-, {1,2}-, {1,3}-, {1,4}- and MP-inverses of Ore matrices, and give some explicit formulas for these inverses. Using {1}-inverses of Ore matrices, we present the solutions of linear systems over Ore polynomial rings. Next, we extend Roth's Theorem 1 and generalized Roth's Theorem 1 to the Ore matrices case. Furthermore, we consider the extensions of all the involutions ψ on R(x), and construct some necessary and sufficient conditions for ψ to be an involution on R(x)[D;σ,δ]. Finally, we obtain two different explicit formulas for {1,3}- and {1,4}-inverses of Ore matrices. The Maple implementations of our main algorithms are presented in the Appendix. | en_US |
| dc.description.note | May 2017 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/32173 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | Generalized inverses | en_US |
| dc.subject | Skew polynomial rings | en_US |
| dc.title | Generalized inverses of matrices over skew polynomial rings | en_US |
| dc.type | master thesis | en_US |